[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
fuzzy longness
xorxes cusku di'e
>In spite of what I said before, I think it should be {le ka clani},
>not {le clani}. As Goran pointed out, a property can't be long.
But <le ka clani> translates as "the property of length" doesn't it?
>Also, note that {pafi'ucisi'e} is a brivla, not a number. This is not
>how {xoi} was supposed to work in And's proposal. You just need
>{pafi'uci xoi}.
You're right.
How about something like:
ti pafi'uci xoi barda ka clani le cnano
ta refi'uci xoi barda ka clani le cnano
tu cifi'uci xoi barda ka clani le cnano
"This is to fuzzy extent 1/3 big-lengthed compared to normal."
"That is to fuzzy extent 2/3 big-lengthed compared to normal."
"That yonder is to fuzzy extent 3/3 big-lengthed compared to normal."
The fuzzy sets are not explicitly given in these statements. More explicit
statements would give the sets explicitly.
>> I also believe
>> that in moving from an ordinal scale (slightly, moderately, extremely) to
>> an interval scale, that the universe of potential discourse is enriched in
>> a very important way.
>
>It is enriched. If you say that 1/3-big, 2/3-big, and 3/3-big constitute
>an interval scale, you are saying that the difference in tallness between
>the extremely tall and the moderately tall is the same as that between
>the moderately tall and the slightly tall. Is that true?
>
I don't mean to imply that, and I think we agree its not true. Here's what
I want to do: Suppose I am using a 3-granularity fuzzy scale. Suppose
speaker and listener sample a population and find the average height is 160
cm. Speaker & listener then agree that:
0/3 fuzzily tall is the triangle {{0,1},{160,1},{175,0}}
1/3 fuzzily tall is the triangle {{160,0},{175,1},{190,0}}
2/3 fuzzily tall is the triangle {{175,0},{190,1},{205,0}}
3/3 fuzzily tall is the "triangle" {{190,0},{205,1},{Infinity,1}}
So it is the *apices* of the fuzzy sets, {160,175,190,205} which form an
interval scale. Note that the sets overlap, and that a person of any height
between apices is partially in two sets. This is typical fuzzy stuff.
>> >Why not give examples using {melbi} rather than {clani}, which has no
>> >objective counterpart to rely on.
>> <clani> is simpler to explain, and people are less emotional about height
>> than beauty.
>
>If you get emotional about the beauty of people think instead of the
>beauty of flowers. Let's say that we agree that a rose has 3/4-beuty and
>another rose has 1/2-beauty. Does our agreement on those two points give
>us a scale to determine the beauty of a third rose? Isn't it possible
>that you will think the third rose is 1/4-beautiful and I would think
>it is 1-beautiful?
I have no objection to attempting to come up with a mutually agreeable
interval scale for the beauty of roses. I think it would be hard, but I see
no reason why it couldn't be done.
>
>> Clarity is served through the use of a simple example as a
>> demonstration of proof of concept.
>
>I love examples, but you can't get attached to a single one. If your
>theory is general it should work for different cases.
We agree.
>I claim that your
>theory for fuzzy tallness (the way you present it) is completely based
>on the objective notion of measurement.
We agree, with the caveat that I believe that it will often be unnecessary
to explicitly specify the exact apices and bases of the fuzzy sets, as
there will be enough inherent consensus to communicate meaningfully with
implicit fuzzy sets as long as the granularity is explicit.
>If it is more general, it should
>also work for properties like beauty that have no objective notion
>behind it.
Agreed.
>
>> >Dividing a continuous
>> >spectrum into a discrete set can always be done, but that is not what
>> >fuzzy truth values are about.
>>
>> We're dividing the continuous spectrum into fuzzy sets, not discrete sets.
>
>Ok. My question is what to do when you don't have an objective continuous
>spectrum from which to define the fuzzy sets.
Make one.
>
>> Even if klani works (fuzzy meter zone =
>> <klanimitreranji>?) it might be useful to have a separate word for fuzzy.
>
>What place structure do you have in mind for it? Perhaps a lujvo can
>be made. I have no idea what you mean by "fuzzy meter zone", but the
>lujvo in any case would be {klanymitryranji}.
>
>> We still need a formalism for handling numbers, like in this example:
>>
>> la xorxes pafi'ucisi'e xoi <fudjimitreranji [1.6,2.0]>
>
>What does it mean?
>
> Jorge 1/3 fuzzy-meter-continuous [1.6,2.0]
>
>Does that mean that the truth value of "Jorge is fuzzy-meter-continuous
>[1.6,2.0]" is 1/3? That was And's original idea for {xoi}, but I don't
>know if you are using it like that.
I now think the <fudji> or <klani> as used in <fudjimitreranji> is
redundant, as this work is being done by <xoi> but I believe we still need
<barda>.
The fuzzy zone is distinct from the two non-fuzzy zones:
height < 1.6 meters, is entirely 0/3 tall and not at all 1/3 tall
height > 2.0 meters is entirely 3/3 tall and not at all 2/3 tall
If 1.6 meters < height < 2.0 meters, you are in the fuzzy zone. The
granularity is three, which means that there are four fuzzy set apices, two
at the ends, and two evenly distributed within the interval 1.6 to 2.0. at
the 1/3 and 2/3 positions.
la xorxes pafi'uci xoi barda ka clani le <mitryranji [1.6,2.0]>
"xorxes is in the first of three equal-interval fuzzy sets within the fuzzy
zone that begins at 1.6 meters and ends at 2.0 meters." Thus, the new
<mitryranji> thing fills the X3 position of <barda>.
co'o mi'e. la stivn.
Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria
email: sbelknap@uic.edu
Voice: 309/671-3403
Fax: 309/671-8413